%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:45:20 AM UTC 2026
% Result : Theorem 15.84s 2.57s
% Output : CNFRefutation 15.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 79 ( 43 unt; 0 def)
% Number of atoms : 194 ( 94 equ)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 191 ( 76 ~; 76 |; 22 &)
% ( 10 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 4 con; 0-3 aty)
% Number of variables : 157 ( 15 sgn 67 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_tarski,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = B
| D = A ) ) ),
file('theBenchmark.p',d2_tarski) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d4_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_dom(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(C,D),A) ) ) ),
file('theBenchmark.p',d4_relat_1) ).
fof(d4_xboole_0,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('theBenchmark.p',d4_xboole_0) ).
fof(d5_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( B = relation_rng(A)
<=> ! [C] :
( in(C,B)
<=> ? [D] : in(ordered_pair(D,C),A) ) ) ),
file('theBenchmark.p',d5_relat_1) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(d6_relat_1,axiom,
! [A] :
( relation(A)
=> relation_field(A) = set_union2(relation_dom(A),relation_rng(A)) ),
file('theBenchmark.p',d6_relat_1) ).
fof(l1_zfmisc_1,axiom,
! [A] : singleton(A) != empty_set,
file('theBenchmark.p',l1_zfmisc_1) ).
fof(t1_boole,axiom,
! [A] : set_union2(A,empty_set) = A,
file('theBenchmark.p',t1_boole) ).
fof(t2_boole,axiom,
! [A] : set_intersection2(A,empty_set) = empty_set,
file('theBenchmark.p',t2_boole) ).
fof(t3_boole,axiom,
! [A] : set_difference(A,empty_set) = A,
file('theBenchmark.p',t3_boole) ).
fof(t48_xboole_1,axiom,
! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
file('theBenchmark.p',t48_xboole_1) ).
fof(t69_enumset1,axiom,
! [A] : unordered_pair(A,A) = singleton(A),
file('theBenchmark.p',t69_enumset1) ).
fof(t30_relat_1,conjecture,
! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t30_relat_1) ).
fof(t30_relat_1_neg,negated_conjecture,
~ ! [A,B,C] :
( relation(C)
=> ( in(ordered_pair(A,B),C)
=> ( in(B,relation_field(C))
& in(A,relation_field(C)) ) ) ),
inference(assume_negation,[status(cth)],[t30_relat_1]) ).
cnf(c_165,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_166,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
fof(nnf_12,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( D != B
& D != A )
| ~ in(D,C) )
& ( D = B
| D = A
| in(D,C) ) )
| unordered_pair(A,B) = C )
& ( ! [X0] :
( ( ( X0 != B
& X0 != A )
| in(X0,C) )
& ( X0 = B
| X0 = A
| ~ in(X0,C) ) )
| unordered_pair(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d2_tarski]) ).
fof(sk_d2_tarski_sk,plain,
! [A,B,C] :
( ( ( ( ( sK0(A,B,C) != B
& sK0(A,B,C) != A )
| ~ in(sK0(A,B,C),C) )
& ( sK0(A,B,C) = B
| sK0(A,B,C) = A
| in(sK0(A,B,C),C) ) )
| unordered_pair(A,B) = C )
& ( ! [X0] :
( ( ( X0 != B
& X0 != A )
| in(X0,C) )
& ( X0 = B
| X0 = A
| ~ in(X0,C) ) )
| unordered_pair(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_12]) ).
fof(sk_d2_tarski,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) != VAR_1
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) != VAR_0
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( sK0(VAR_0,VAR_1,VAR_2) = VAR_1
| sK0(VAR_0,VAR_1,VAR_2) = VAR_0
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| unordered_pair(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_1
| in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 != VAR_0
| in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_3 = VAR_1
| VAR_3 = VAR_0
| ~ in(VAR_3,VAR_2)
| unordered_pair(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d2_tarski_sk]) ).
cnf(c_200,plain,
( sK0(A,B,C) = B
| sK0(A,B,C) = A
| in(sK0(A,B,C),C)
| unordered_pair(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d2_tarski]) ).
cnf(c_204,plain,
( ~ in(D,A)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
cnf(c_228,plain,
( ~ in(ordered_pair(C,D),A)
| in(C,B)
| relation_dom(A) != B
| ~ relation(A) ),
inference(clausify,[status(thm)],[d4_relat_1]) ).
cnf(c_239,plain,
( ~ in(D,B)
| ~ in(D,C)
| set_difference(A,B) != C ),
inference(clausify,[status(thm)],[d4_xboole_0]) ).
cnf(c_245,plain,
( ~ in(ordered_pair(D,C),A)
| in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(clausify,[status(thm)],[d5_relat_1]) ).
cnf(c_249,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_250,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,B)),
inference(paramod,[status(thm)],[c_165,c_249]) ).
cnf(c_251,plain,
( relation_field(A) = set_union2(relation_dom(A),relation_rng(A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[d6_relat_1]) ).
cnf(c_281,plain,
singleton(A) != empty_set,
inference(clausify,[status(thm)],[l1_zfmisc_1]) ).
cnf(c_325,plain,
set_union2(A,empty_set) = A,
inference(clausify,[status(thm)],[t1_boole]) ).
cnf(c_339,plain,
set_intersection2(A,empty_set) = empty_set,
inference(clausify,[status(thm)],[t2_boole]) ).
cnf(c_353,plain,
set_difference(A,empty_set) = A,
inference(clausify,[status(thm)],[t3_boole]) ).
cnf(c_369,plain,
set_difference(A,set_difference(A,B)) = set_intersection2(A,B),
inference(clausify,[status(thm)],[t48_xboole_1]) ).
cnf(c_370,plain,
set_intersection2(A,B) = set_difference(A,set_difference(A,B)),
inference(copy,[status(thm)],[c_369]) ).
cnf(c_383,plain,
singleton(A) = unordered_pair(A,A),
inference(clausify,[status(thm)],[t69_enumset1]) ).
fof(nnf_148,plain,
? [A,B,C] :
( ( ~ in(B,relation_field(C))
| ~ in(A,relation_field(C)) )
& in(ordered_pair(A,B),C)
& relation(C) ),
inference(fof_nnf,[status(thm)],[t30_relat_1_neg]) ).
fof(sk_t30_relat_1_neg,plain,
( ( ~ in(sK3,relation_field(sK1))
| ~ in(sK2,relation_field(sK1)) )
& in(ordered_pair(sK2,sK3),sK1)
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK1)],[nnf_148]) ).
cnf(c_398,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t30_relat_1_neg]) ).
cnf(c_399,negated_conjecture,
in(ordered_pair(sK2,sK3),sK1),
inference(split_conjunct,[status(thm)],[sk_t30_relat_1_neg]) ).
cnf(c_8047,negated_conjecture,
in(unordered_pair(singleton(sK2),unordered_pair(sK2,sK3)),sK1),
inference(paramod,[status(thm)],[c_250,c_399]) ).
cnf(c_400,negated_conjecture,
in(unordered_pair(unordered_pair(sK2,sK2),unordered_pair(sK2,sK3)),sK1),
inference(paramod,[status(thm)],[c_383,c_8047]) ).
cnf(c_401,negated_conjecture,
( ~ in(sK3,relation_field(sK1))
| ~ in(sK2,relation_field(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t30_relat_1_neg]) ).
cnf(c_429,plain,
( ~ in(C,B)
| set_difference(A,B) != B ),
inference(factor,[status(thm)],[c_239]) ).
cnf(c_8048,plain,
( ~ in(unordered_pair(singleton(D),unordered_pair(D,C)),A)
| in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_250,c_245]) ).
cnf(c_435,plain,
( ~ in(unordered_pair(unordered_pair(D,D),unordered_pair(D,C)),A)
| in(C,B)
| relation_rng(A) != B
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_383,c_8048]) ).
cnf(c_8049,plain,
( ~ in(unordered_pair(singleton(C),unordered_pair(C,D)),A)
| in(C,B)
| relation_dom(A) != B
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_250,c_228]) ).
cnf(c_439,plain,
( ~ in(unordered_pair(unordered_pair(C,C),unordered_pair(C,D)),A)
| in(C,B)
| relation_dom(A) != B
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_383,c_8049]) ).
cnf(c_8050,plain,
set_difference(A,set_difference(A,empty_set)) = empty_set,
inference(paramod,[status(thm)],[c_370,c_339]) ).
cnf(c_462,plain,
set_difference(A,A) = empty_set,
inference(paramod,[status(thm)],[c_353,c_8050]) ).
cnf(c_490,plain,
unordered_pair(A,A) != empty_set,
inference(paramod,[status(thm)],[c_383,c_281]) ).
cnf(c_532,plain,
~ in(A,empty_set),
inference(resolve,[status(thm)],[c_429,c_462]) ).
cnf(c_709,plain,
( sK0(A,B,empty_set) = B
| sK0(A,B,empty_set) = A
| unordered_pair(A,B) = empty_set ),
inference(resolve,[status(thm)],[c_200,c_532]) ).
cnf(c_8051,plain,
( sK0(A,A,empty_set) = A
| unordered_pair(A,A) = empty_set ),
inference(factor,[status(thm)],[c_709]) ).
cnf(c_738,plain,
sK0(A,A,empty_set) = A,
inference(resolve,[status(thm)],[c_490,c_8051]) ).
cnf(c_840,plain,
( ~ in(A,C)
| in(A,set_union2(B,C)) ),
inference(resolve,[status(thm)],[c_204,c_166]) ).
cnf(c_8052,plain,
A = sK0(A,A,empty_set),
inference(copy,[status(thm)],[c_738]) ).
cnf(c_8053,plain,
( ~ in(A,B)
| in(A,sK0(set_union2(B,C),set_union2(B,C),empty_set)) ),
inference(resolve,[status(thm)],[c_204,c_8052]) ).
cnf(c_841,plain,
( ~ in(A,B)
| in(A,set_union2(B,C)) ),
inference(paramod,[status(thm)],[c_738,c_8053]) ).
cnf(c_2094,plain,
relation_field(sK1) = set_union2(relation_dom(sK1),relation_rng(sK1)),
inference(resolve,[status(thm)],[c_251,c_398]) ).
cnf(c_8054,negated_conjecture,
( ~ in(sK3,relation_field(sK1))
| ~ in(sK2,set_union2(relation_dom(sK1),relation_rng(sK1))) ),
inference(paramod,[status(thm)],[c_2094,c_401]) ).
cnf(c_2095,negated_conjecture,
( ~ in(sK3,set_union2(relation_dom(sK1),relation_rng(sK1)))
| ~ in(sK2,set_union2(relation_dom(sK1),relation_rng(sK1))) ),
inference(paramod,[status(thm)],[c_2094,c_8054]) ).
cnf(c_8055,plain,
A = set_union2(empty_set,A),
inference(paramod,[status(thm)],[c_325,c_166]) ).
cnf(c_3564,plain,
set_union2(empty_set,A) = A,
inference(copy,[status(thm)],[c_8055]) ).
cnf(c_8056,negated_conjecture,
( in(sK3,A)
| relation_rng(sK1) != A
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_435,c_400]) ).
cnf(c_7798,negated_conjecture,
( in(sK3,A)
| relation_rng(sK1) != A ),
inference(resolve,[status(thm)],[c_398,c_8056]) ).
cnf(c_8057,plain,
A = set_union2(empty_set,A),
inference(copy,[status(thm)],[c_3564]) ).
cnf(c_8058,plain,
in(sK3,set_union2(empty_set,relation_rng(sK1))),
inference(resolve,[status(thm)],[c_7798,c_8057]) ).
cnf(c_7912,plain,
in(sK3,relation_rng(sK1)),
inference(paramod,[status(thm)],[c_3564,c_8058]) ).
cnf(c_7926,plain,
in(sK3,set_union2(A,relation_rng(sK1))),
inference(resolve,[status(thm)],[c_7912,c_840]) ).
cnf(c_7979,negated_conjecture,
~ in(sK2,set_union2(relation_dom(sK1),relation_rng(sK1))),
inference(resolve,[status(thm)],[c_7926,c_2095]) ).
cnf(c_8059,negated_conjecture,
( in(sK2,A)
| relation_dom(sK1) != A
| ~ relation(sK1) ),
inference(resolve,[status(thm)],[c_439,c_400]) ).
cnf(c_7995,negated_conjecture,
( in(sK2,A)
| relation_dom(sK1) != A ),
inference(resolve,[status(thm)],[c_398,c_8059]) ).
cnf(c_8060,plain,
A = set_union2(empty_set,A),
inference(copy,[status(thm)],[c_3564]) ).
cnf(c_8061,plain,
in(sK2,set_union2(empty_set,relation_dom(sK1))),
inference(resolve,[status(thm)],[c_7995,c_8060]) ).
cnf(c_8032,plain,
in(sK2,relation_dom(sK1)),
inference(paramod,[status(thm)],[c_3564,c_8061]) ).
cnf(c_8045,plain,
in(sK2,set_union2(relation_dom(sK1),A)),
inference(resolve,[status(thm)],[c_8032,c_841]) ).
cnf(c_8046,plain,
$false,
inference(resolve,[status(thm)],[c_8045,c_7979]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU180+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.46 % Computer : n007.cluster.edu
% 0.19/0.46 % Model : x86_64 x86_64
% 0.19/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.46 % Memory : 8046.5625MB
% 0.19/0.46 % OS : Linux 6.8.0-71-generic
% 0.19/0.46 % CPULimit : 300
% 0.19/0.46 % WCLimit : 300
% 0.19/0.46 % DateTime : Sat Sep 26 08:43:25 UTC 2026
% 0.19/0.47 % CPUTime :
% 0.19/0.47 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.47 % Process 3330382 was started by sandbox on n007,
% 0.19/0.47 % Sat Sep 26 08:43:25 2026
% 0.19/0.47 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.24/0.52
% 0.24/0.52 % From the command line: assign(max_seconds, 300).
% 0.24/0.52
% 0.24/0.52 % SInE: 128 to sos, 21 to usable, of 149 axioms (tolerance 2.00, depth 0 fixpoint).
% 15.84/2.57
% 15.84/2.57 % given #500 (F,wt=15): 4899 -disjoint(powerset(A),f37(empty_set)). [resolve(4702,a,154,a)].
% 15.84/2.57
% 15.84/2.57 % SZS status Theorem for theBenchmark
% 15.84/2.57
% 15.84/2.57 % Proof 1 at 1.56 (+ 0.44) seconds.
% 15.84/2.57 % Length of proof is 58.
% 15.84/2.57 % Level of proof is 9.
% 15.84/2.57 % Maximum clause weight is 229.000.
% 15.84/2.57 % Given clauses 727.
% 15.84/2.57
% 15.84/2.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------